Simplify the following expression: $ r = \dfrac{-10}{9} - \dfrac{z - 10}{-2z} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2z}{-2z}$ $ \dfrac{-10}{9} \times \dfrac{-2z}{-2z} = \dfrac{20z}{-18z} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{z - 10}{-2z} \times \dfrac{9}{9} = \dfrac{9z - 90}{-18z} $ Therefore $ r = \dfrac{20z}{-18z} - \dfrac{9z - 90}{-18z} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{20z - (9z - 90) }{-18z} $ Distribute the negative sign: $r = \dfrac{20z - 9z + 90}{-18z}$ $r = \dfrac{11z + 90}{-18z}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-11z - 90}{18z}$